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Discrete optimization is a branch of optimization in applied mathematics and computer science. As opposed to continuous optimization , some or all of the variables used in a discrete optimization problem are restricted to be discrete variables —that is, to assume only a discrete set of values, such as the integers .
Optimization problems can be divided into two categories, depending on whether the variables are continuous or discrete: An optimization problem with discrete variables is known as a discrete optimization, in which an object such as an integer, permutation or graph must be found from a countable set.
Written in C/C++ and Fortran with gateways to Excel, VBA, Java, Python, Matlab, Octave, R, C#, and Julia. Mathematica – large-scale multivariate constrained and unconstrained, linear, quadratic and nonlinear, continuous, and integer optimization. ModelCenter – a graphical environment for integration, automation, and design optimization.
In mathematics and statistics, a quantitative variable may be continuous or discrete if it is typically obtained by measuring or counting, respectively. [1] If it can take on two particular real values such that it can also take on all real values between them (including values that are arbitrarily or infinitesimally close together), the variable is continuous in that interval. [2]
Continuous optimization is a branch of optimization in applied mathematics. [ 1 ] As opposed to discrete optimization , the variables used in the objective function are required to be continuous variables —that is, to be chosen from a set of real values between which there are no gaps (values from intervals of the real line ).
In the logistic map, r is a parameter, and x is a variable. It is a map in the sense that it maps a configuration or phase space to itself (in this simple case the space is one dimensional in the variable x)
Solving topology optimization problems in a discrete sense is done by discretizing the design domain into finite elements. The material densities inside these elements are then treated as the problem variables. In this case material density of one indicates the presence of material, while zero indicates an absence of material.
Discrete choice models theoretically or empirically model choices made by people among a finite set of alternatives. The models have been used to examine, e.g., the choice of which car to buy, [1] [3] where to go to college, [4] which mode of transport (car, bus, rail) to take to work [5] among numerous other applications. Discrete choice ...